Reasoning about parallel networks: Six resistors are connected in parallel. The two smallest values are both 1.2 kΩ. What can you conclude about the total equivalent resistance?

Introduction / Context:
Understanding limits on equivalent resistance helps you quickly sanity-check parallel networks without full calculation. With multiple branches, the equivalent is strongly influenced by the smallest resistances because conductances add in parallel.

Given Data / Assumptions:

• Six resistors in parallel (values unspecified except two are 1.2 kΩ).
• All branches connect across the same voltage.
• Ideal components (no parasitics) for reasoning.

Concept / Approach:

For any parallel network, R_eq is less than or equal to the smallest branch resistance, and adding any additional finite branch strictly decreases R_eq. Two equal resistors R in parallel give R/2. Additional branches further decrease R_eq.

Step-by-Step Solution:

Verification / Alternative check:

Even if the remaining four resistors were very large (but finite), they would still reduce the equivalent below 600 Ω, though perhaps only slightly.

Why Other Options Are Wrong:

'is less than 1.2 kΩ' is true but not the strongest conclusion. 'is greater than 1.2 kΩ' and 'equals 1.2 kΩ' contradict parallel rules. 'is less than 6 kΩ' is trivially true and uninformative compared with the tighter bound 600 Ω.

Common Pitfalls:

Adding resistances instead of conductances; forgetting that even very large added resistances still reduce R_eq (though by a small amount).

Final Answer:

is less than 600 Ω